10-Valence-Electron C≡O and the 14-VE C≡Pt: Two Triple-Bonded Isoelectronic Families Differing by a dδ4 Ring

10-VE A≡A′ Diatomics, such as N≡N, C≡O, etc., have a strong σ2π4 triple bond plus a lone pair at each end. In our studies on 14-VE A≡B systems, such as C≡Pt, we find a similar bonding system plus a (5dδ)4 ring. Here, the A atom belongs to groups 13–17 and the B atom to groups 7–11. Also the BB′ combinations, triatomics, such as PtCO or DsCO or uranyl, and longer chains, such as AuCN and [NC-Au-CN]−, are discussed. The δ ring directly contributes to nuclear quadrupole coupling constants, and DFT calculations using the BH and H or mPW1K functionals reproduce the experimental trends of the NQCC.


INTRODUCTION
While developing a set of additive covalent triple-bond radii, r 3 ,1,2 the same covalent radii r(A) were used in fitting the maingroup A�A′ and the A�B bond lengths, where B is a transition metal.The primary bond lengths came from experimental or computed closed-shell systems with main-group elements and with transition metals as long as the molecular-orbital inspection and the actual bond length fitted the picture.The same covalent radii r(A) were used in fitting the main-group A�A′ and the A�B bond lengths for both single, double, and triple bonds, r 1 , r 2 , and r 3 , respectively.
In our ongoing calculations, we kept finding two different sets of diatomic species.One was the well-known 10VE family of diatomic systems, such as N 2 , CO, CN − , NO + , etc.These are known to have a nominal σ 2 π4 triple bond combined with a lone electron pair at each end.In all, we then have 10 valence electrons (10VE) 3 (it should be noticed that, as an alternative to this triple-bond picture, in older literature, a C�O double bond was thought to exist, and also other resonance hybrids have been mentioned, see Pauling 4 or Long and Walsh 5 ).
The other families, such as CPt, X 1 Σ had four more electrons, always occupying a δ 4 ring, typically the penultimate, HOMO − 1.With this, we mean the occupied (d xy ) 2 (d x 2 −y 2 ) 2 combination, in an alternative form d l m ( 2, 2) , or (dδ) 4 .The novelty is that we have an occupied orbital which is formally a nonbonding core orbital but has the size and orbital energy of a typical valence orbital.That observation is not new, and some previous examples are shown in Table 1.We are, however, not aware of any previous articles concentrating on this feature.
Starting from these 10-VE or 14-VE families of species, we made some further contacts:

METHODS
We use in the present calculations DFT and ZORA at either the scalar relativistic (SR) or spin−orbit (SO) level.This will provide reasonable accuracy and easy interpretation of chemical bonding questions.
The calculations were carried out by using the ADF software package 15 with the Perdew−Burke−Ernzerhof (PBE) functional during the structural calculations.The triple-ζ basis sets with two polarization functions (TZ2P) were used for all elements, treated at the nonfrozen core level.
We have added into Tables 2, 3, 4, 5, and 6 the results of some earlier calculations and a comparison with the sum a of our triple-bond covalent radii r 3 . 1,22 gives the bond lengths of the A�B diatomics, specified in Figure 1, mostly for 14VE species.

Diatomics. Table
These AB R e values in Table 2 are close to the sum of triplebond covalent radii.To the contrary, the BB′ ones in Table 3 can be much shorter, reflecting a bond order higher than three.Quadruple bonding in ground or excited states of certain AB diatomics 20,25 and BB systems 6 has also been discussed.
Liu et al. 26 consider the donation and its direction in certain multiply bonded AA′ diatomics.Cheung et al. 16 also discuss 4fold bonding in RhB.The MU species (M = Cr−W) of Ruipeŕez et al. 27 have the δ ring as the HOMO, see Table 3.Note that at the scalar relativistic level, these are 12-VE species with a (1π) 4 (1σ) 2 (2σ) 2 (1δ) 4 X 1 Σ ground state, see ref 27 Figure 1.

Polyatomic Chains.
If group 11 (Cu, Ag, Au, and Rg) doubles as a halogen and group 10 (Ni, Pd, Pt, and Ds) as a chalcogen, it is easy to take the step from OCO to PtCO or DsCO. 12With metals at both ends, we have [Au�C�Au] 2+ , or the analogues CPt, CPt 2 , and CPt 3 2− to CO, CO 2 , and CO 3 2− , respectively. 30f the species in Table 4, the triatomic PtCPt and [AuCAu] 2+ have two δ 4 rings, both a g and a u one, separated from each other by the carbon atom.
Similarly, the uranyl isoelectronic series 31 would yield NUN and the NUIr of Gagliardi and Pyykko. 32The NUO + predicted by Pyykköet al. 31 was later made by Heinemann and Schwarz 33 in the gas phase and by Zhou and Andrews 34 in Ne matrices.The OUIr + was prepared by Santos et al. 35 For reviews on uranyl analog complexes, see Wei et al., 36 or Maria and Marcalo. 37A closer analysis of U�A multiple bonding was given by Motta and Autschbach. 38ith 5d metals at both ends, linear species like PtThIr − were found by Hrobaŕik et al. 39 This species had a δ 4 ring at the Pt    end, and some evidence for Th−Ir δ bonding at the Ir end.Two of the σ bonds were characterized as "a sausage inside a tube".
The isoelectronic series of [ClAuCl] − can be continued at least to the high-pressure compound Li 5 AuP 2 . 40The energetic location of the δ 4 ring in the [XAuX] − series, X = F−At, is discussed in the last column of Table 4. , an assigned quadruple-bond case.For further examples, see the book. 6He also found two triple U�O bonds in uranyl.Possible members of the uranyl isoelectronic series down to [CUC] 2− have been discussed. 31ost of the World's gold production 42 is based on the [NC-Au-CN] − ion, which has a beautiful δ ring, as seen from Figure 2.This δ energy level occurred as H-2 also in earlier calculations. 43he [XAuX] − experimental values for X = Cl−I are taken from. 44In the last column, the δ gives the energetic placement of the dδ 4 MO with respect to the HOMO (H).Slight variations of the order may occur as a function of the method.PW: Present work.    2 and 3, the present R mostly agree with for triple bonds.The higher bond-orders in Table 3 may be substantially shorter.Clear trends as a function of the group and the row are seen in Figure 3.For the shortness of the n = 2 radii, see Wang et al. 52 Note for the n-dependence of the main-group elements A the clear trend 2 ≪ 3 < 4 < 5 < 6, while the transition metals, B, in the groups 9−10 rather have 6 < 5 ≈ 4. The sixth-row elements near gold have a local maximum of the relativistic bond-length contraction. 53ibrational frequencies are another direct connection to experiments.As examples, we can take Table 5 on diatomics or Table 6 on polyatomic chains.
Dissociation energies and predissociation of species like CuB, AuB, or AlB are discussed by Merriles and Morse. 58The δ MO is quoted in their Supporting Information.
Nuclear quadrupole coupling constants, NQCCs, give a direct access to the electric field gradient, q at the nuclei involved.The four electrons in the δ 4 ring make a major contribution.The RuC has been mentioned as an example by Wang et al., 19 who estimate that +1350 MHz of the experimental B 0 of +433 MHz of 101 RuC come from the δ 4 ring.Without this contribution, even the sign would be wrong.Gusmaõ et al. 59 obtained similar q values for RuC.b For nuclear quadrupole coupling constants, BHandH and mPW1K functionals were applied.The BHandH gave earlier good q for HCl and CuCl, 60 CdMe 2 , 61 and Cd(SMe) 2 . 62n early multiple-scattering Xα calculations, Bowmaker et al. 14 gave an orbital-based analysis of their q and found for [Au(CN) 2 − ] that about +15.805 of the total q of −9.650 au arise from the H-4 δ 4 electrons.They emphasized in their scalarrelativistic discussion of the AuX 2 − species the q contributions from the Au 6p z orbital.
In the linear HAuH − both the Au 5dπ and 5dδ would be "inert" and only the Au 6s and 5dσ participate in bonding, as seen from Figure 4. In actual fact, one must emphasize that the XAuX − calculations show some unusually strong dependence on the chosen functional. 57Moreover, the Mossbauer measurements are performed on solid samples with so far unknown matrix effects.
The gas-phase measurements included in Tables 7 and 8 have a chance to provide cleaner comparisons.The gas-phase microwave quadrupole coupling constants of Okabayashi et al. 65 for triatomic AuCN were in complete disagreement with our earlier calculations, while their structural and vibrational AuCN parameters are in adequate agreement both with our more approximate work, and the latest and best studies. 56,66hen, we found that the alternative functionals BHandH and mPW1K gave a semiquantitative agreement between the experimental and calculated B, as seen from Figure 5.
As one point of reference, the neutral Au atom in a 5d 9 6s 22 D 5/2 state has a B of −1049.781(11) MHz. 67In other words, one d −1 hole gives a GHz.Many of the red dots in Figure 5 are far smaller than that.
Wang 46 observed photoelectron spectra in [Au(CN) 2 ] − (g) and found in calculations significant covalent character in the Au−C bond.

Recent Further
Examples on δ 4 Rings.Kalita et al. 82 suggest RhSc as a sextuply bonded diatomic with a Rh → Sc δ HOMO.Likewise, Tzeli and Karapetsas 20 find X 1 Σ + ground states for RuC, RhB, and PdBe, all three having nonbonding δ 4 HOMOs.For systems of the [MUM] type with M = Rh, Ir, see Shen et al. 83 and references there.

CONCLUSIONS
The δ 4 ring lies energetically and radially in the valence range of the 5d elements discussed despite being formally a filled core orbital. 81Yet it yields mostly no covalent bonding contributions, although the Coulomb attraction to the neighbors must be substantial.In its way, this δ 4 ring resembles the σ 2 lone pairs.An open question is, what kind of chemistry could one do with the δ 4 ?
r 3 : From triple-bond covalent radii.b SR. c SO.

Figure 1 .
Figure 1.Schematic placement of the main-group elements (A) and transition elements (B).The 10VE A�A′ and 14VE A�B combinations are indicated.l.p. = lone pairs.

Figure 5 .
Figure 5.Comparison between calculated (PW) and experimental B. The data are taken from Tables7 and 8.The red dots refer to B(Au) and the blue dots refer to other nuclei.

Table 2 .
Calculated and Experimental Bond Lengths, R e , for AB Diatomics a a δ gives the energetic placement of the dδ 4 MO with respect to the HOMO (H)."PW": Present work.r 3 : From triple-bond covalent radii. 1,2b SR. c SO. d 12VE species.e R 0 .

Table 3 .
Calculated and Experimental Bond Lengths, R e for BB′ Diatomics a δ gives the energetic placement of the dδ 4 MO with respect to the HOMO (H).PW: Present work. a

Table 4 .
Calculated and Experimental Bond Lengths, R e , for Linear Polyatomic Species a